Logic full adder circuit

ABSTRACT

A logic circuit incorporating carry look-ahead in which efficiency can be achieved regarding the hardware for generating the sum signals and carry signals by a suitable choice of the adder gate, making use of the already present signal a 1  ·b i  which is used for generating the carry look-ahead signal.

BACKGROUND OF THE INVENTION

The invention relates to a logic full-adder circuit for adding two binary numbers a and b which each consist of n bits, n being a natural number larger than or equal to 2. The full adder comprises an inverting OR-gate and an inverting AND-gate for each bit a_(i), b_(i) of the numbers a and b, where 0≦i≦n, said gates receiving the bit signals a_(i) and b_(i) in order to form an inverted OR-signal a_(i) +b_(i) and an inverted AND-signal a_(i) ·b_(i).

A summing circuit forms a sum signal s_(i) from the bit signals a_(i) and b_(i) and an associated carry signal c_(i) and/or the inverse c_(i) thereof. The full-adder circuit also comprises a carry look-ahead signal circuit for generating a carry look-ahead signal c_(n+1) having the significance n+1 from all inverted OR-signals and AND-signals a_(i) +b_(i) and a_(i) ·b_(i) where 0≦i≦n.

Such full-adder circuits are marketed in the form of integrated circuits by various firms, for example Signetics type SN 7483 or Motorola type MC14008. These circuits utilize the principle of forming a carry look-ahead signal from the carry signals produced during the various additions of bits of ascending significance. The carry look-ahead signal has the correct logic value for being applied to the adder gates of the bits of higher significance than the next-higher significance. If the bits of ascending significance of the signals a and b are successively denoted as a_(o), a₁, a₂ etc. and b_(o), b₁, b₂ etc. the carry signal c₁ would, before the introduction of the carry look-ahead principle, have been formed from the addition a_(o) +b_(b), said carry signal being applied to the adder gate of the signals a₁ and b₁, the carry signal c₂ formed during this addition being subsequently applied to the adder gate of the signals a₂ and b₂ etc. so that the addition in the n^(th) gate of the signals a_(n) and b_(n) could not be started before completion of the additions in all preceding gates. By generating the carry look-ahead signal c_(n) in advance in some other way in accordance with the carry look-ahead principle, the speed of calculation can be substantially increased.

To this end, the known circuits utilize a separate arithmetic unit containing a truth table such that when the signals a_(o), a₁ . . . a_(n-1) and b_(o), b₁, . . . b_(n-1) are inputted, the output directly supplies the carry look-ahead signal c_(n). In order to generate the carry look-ahead signal, the signals a_(i) +b_(i) and a_(i) ·b_(i) are generated by means of inverting OR-gates and AND-gates. In addition to this carry look-ahead signal circuit, a full-adder circuit comprise, for each bit of a binary number to be added, a summing circuit for generating a sum signal and a carry circuit for generating a carry signal which is required for obtaining the desired higher-order sum signal. It will be apparent that a substantial number of logic gates is required for this purpose.

SUMMARY OF THE INVENTION

It is the object of the invention to provide a full-adder circuit in which the number of logic gates and the number of components (transistors) in these gates can be substantially reduced whilst the result of the addition can become available sooner because the number of delay times has been reduced.

To this end, a full-adder circuit in accordance with the invention is characterized in that each summing circuit comprises a logic gate which receives the bit signals a_(i) and b_(i) and the inverted AND-signal a_(i) ·b_(i) in order to form a logic signal a_(i) ·b_(i) ·(a_(i) +b_(i)) on a first output thereof and the inverted logic signal a_(i) ·b_(i) ·(a_(i) +b_(i)) on a second output thereof, and also comprises electronic switches which connect, under the control of the carry signal c_(i) and/or the inverse c_(i) thereof, either the first output or the second output of the logic gate to a first junction in order to generate an inverted sum signal s_(i) on the first junction.

In addition to the OR-gate and AND-gate already present for the carry look-ahead signal, a full-adder circuit in accordance with the invention may comprise, for each bit of a binary number to be added, only one further logic gate (which needs to comprise only eight transistors in the CMOS transistor technique) and some electronic switches (each of which can comprise, as is known, a field-effect transistor or e.g. in the CMOS technique a parallel connection of a P- and an N-channel transistor). The number of components required is thus substantially reduced, and the delays occuring in the full adder are reduced.

The invention will be described in detail hereinafter with reference to embodiments shown in the drawings.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 shows the construction of a section of a full-adder circuit in accordance with the invention,

FIG. 2 shows an example of a logic gate for a full-adder circuit in accordance with the invention, and

FIG. 3 shows a carry look-ahead signal circuit for a full-adder circuit in accordance with the invention.

DESCRIPTION OF THE PREFERRED EMBODIMENT

FIG. 1 shows a section 10 for a full-adder circuit in accordance with the invention for the processing of one of the bits of the n-bit binary numbers a and b, for example bit a_(i), b_(i). For each bit i there is required a circuit section 10 as shown in FIG. 1. The section 10 comprises an inverting OR-gate 1 and an inverting AND-gate 3 which generate the inverted OR-signal a_(i) +b_(i) and the inverted AND-signal a_(i) ·b_(i). Such gate circuits are known in the state of the art. The section 10 furthermore comprises a sum circuit 20 which comprises a logic gate 5 and electronic switches 7 and 9. The logic gate 5 receives the signals a_(i), b_(i) and a_(i) ·b_(i), on the first output 11 and the second output 13 of the logic gate 5 there being generated the signals (a_(i) ·b_(i))·(a_(i) +b_(i)) and (a_(i) ·b_(i))·(a_(i) +b_(i)) respectively, as will be described in detail hereinafter (with reference to FIG. 2). The outputs 11 and 13 are connected to a first junction 15 via the switches 7 and 9. The switches 7 and 9 are controlled by the carry signal c_(i) and/or the inverse c_(i) thereof, so that on the junction 15 there is formed the sum signal s_(i) which is converted by an inverter 17 connected to the junction 15, into the sum signal s_(i) on an output 19.

In order to obtain the carry signal c_(i+1) and its inverse c_(i+1) which serve to control the switches in a summing section for the summing of bits of the next-higher order, the inverted OR-signal a_(i) +b_(i) and AND-signal a_(i) ·b_(i) are applied to a second junction 25 via switches 21 and 23. On the junction 25 there is obtained the inverted carry signal c_(i+1) which is converted into the carry signal c_(i+1) on output 29 via an inverter 27.

The switches 9 and 21 are N-channel field-effect transistors which are controlled by the carry signal c_(i), the switches 7 and 23 each being a parallel connection of an N- and a P-channel field-effect transistor whose N-channel transistor and P-channel transistor are controlled by the inverted carry signal c_(i) and the carry signal c_(i), respectively.

FIG. 2 shows a logic gate 5 for a full-adder circuit 10 as shown in FIG. 1. The gate 5 is composed of complementary field-effect transistors and comprises an input section 30 and an inverter 40 which is connected to the output which is also shown in FIG. 1. The input section 30 comprises a series connection of two P-channel transistors 31, 32 which are controlled by the signals a_(i) and b_(i) respectively and whereto there is connected in parallel a third P-channel transistor 33 which is controlled by the inverted AND-signal a_(i) ·b_(i). The input section 10 furthermore comprises two parallel-connected N-channel transistors 34, 35 which are controlled by the signals a_(i) and b_(i) respectively and which are connected in series with a third N-channel transistor 36 which is controlled by the inverted AND-signals a_(i) ·b_(i). The junction of the N- and P-channel transistors 32, 33, 34, 35 forms the first output 11 of the logic gate 5 which also comprises a known inverter 40 which comprises complementary transistors 37, 38 and whose input is connected to the first output 11 while its output constitutes the second output 13 of the logic gate 5. On the first output 11 and the second output 13 there are generated the signals (a_(i) ·b_(i))·(a_(i) +b_(i)) and (a_(i) ·b_(i))·(a_(i) +b_(i)), respectively.

FIG. 3 shows a carry look-ahead signal circuit 50 for a full-adder circuit in accordance with the invention. In an n-bit full-adder circuit the circuit 50 receives the inverted OR- and AND-signals a_(i) +b_(i) and a_(i) ·b_(i) wherefrom a carry look-ahead signal c_(n+1) can be derived. This is because:

    c.sub.1 =a.sub.o ·b.sub.o +c.sub.o ·(a.sub.o +b.sub.o)=a.sub.o +b.sub.o +c.sub.o ·(a.sub.o +b.sub.o)

    c.sub.2 =a.sub.1 +b.sub.1 +c.sub.1 ·(a.sub.1 ·b.sub.1)

    c.sub.3 =a.sub.2 +b.sub.2 +c.sub.2 ·(a.sub.2 ·b.sub.2) etc.

It will be apparent from the foregoing that the carry look-ahead signal circuit 50 for the full-adder in accordance with the invention is preferably constructed with complementary field-effect transistors comprising insulated gate electrodes.

The following holds true for a four-bit carry look-ahead signal circuit. The signals a_(i) +b_(i) and a_(i) ·b_(i) are already generated on the outputs of the gates 1 and 3 in the circuit shown in FIG. 1, where 0≦i≦3. The above logic formulae are realized in practice in a simple manner by applying the products a_(i) ·b_(i) of the bits of the input signals a_(i), b_(i) to the inputs of the series-connected N-channel transistors 52-55 with an ascending significance, the sums a_(i) +b_(i) of these bits being applied with an ascending significance to the N-channel transistors 56-59, each of which is connected in parallel with an each time larger section of this series connection. An inverted carry signal c_(o) (carry-in) is applied to the transistor 51. On the connection between the transistor 51 and a P-channel field-effect transistor 60 there is now generated the carry look-ahead signal c₄ which is converted, via a known inverter 70 (comprising a P- and an N-channel field-effect transistor) into an inverted carry look-ahead signal c₄ which could be applied as an input signal to a subsequent cascade-connected full adder. 

What is claimed is:
 1. A logic full adder for adding two binary numbers a and b having n bits each, where n is equal to or greater than 2 including a plurality of single bit adders, each comprising:an inverting AND gate and inverting OR gate for receiving a pair of like bit numbers a_(i) and b_(i) and producing an inverted OR signal a_(i) +b_(i) and an inverted AND signal a_(i) ·b_(i) for each of said pairs of bit numbers; a summing circuit for producing a sum signal from each pair of said like bit numbers a_(i) and b_(i) comprising a logic gate which receives said like bit numbers a_(i), b_(i) and said inverted AND signal a_(i) ·b_(i), and forms on first and second outputs a first signal a_(i) ·b_(i) ·(a_(i) +b_(i)), and a second signal a_(i) ·b_(i) ·(a_(i) +b_(i)), respectively; a pair of electronic switches connected to receive said first and second signals, and operated in response to a carry signal c_(i), to supply either said first signal or said second signal to a first junction; and a carry look-ahead circuit for generating a carry look-ahead signal from said inverted OR signals a_(i) +b_(i) and said inverted AND signals a_(i) ·b_(i) produced by each of said pairs of bit numbers.
 2. The logic full adder of claim 1 further comprising a carry signal circuit which includes a second pair of electronic switches receiving each pair of inverted OR signals a_(i) +b_(i) and inverted AND signals a_(i) ·b_(i) for supplying under control of said carry signal c_(i) either said inverted OR signal or said inverted AND signal to a second junction.
 3. A logic full-adder circuit as claimed in claim 2, which full-adder circuit is constructed with complementary insulated-gate field-effect transistors, the electronic switches together comprise four N-channel field-effect transistors, a first and a second transistor thereof connecting the second and the first output, respectively of the said logic gate, to the first junction, the third and the fourth transistor connecting the output of the inverting OR-gate and the output of the inverting AND-gate, respectively, to the second junction, the first and the third transistor being controlled by the carry signal c_(i) and the second and the fourth transistor being controlled by an inverted carry signal c_(i).
 4. A logic full-adder circuit as claimed in claim 3, further comprising, first and second P-channel field-effect transistors, which are controlled by the carry signal c_(i), connected in parallel with the second and the fourth transistors respectively.
 5. A logic full-adder circuit as claimed in claim 3, wherein two series-connected inverters are connected to the second junction for producing on the outputs thereof a carry signal c_(i+1) and the inverted carry signal c_(i+1) hving the significance i+1, respectively.
 6. A logic full-adder circuit as claimed in claims 3, 4 or 5, wherein each logic gate comprises: a serious connection of two P-channel transistors which receive the bit signals a_(i) and b_(i), respectively, on their gate electrodes, a further P-channel transistor which is connected in parallel with the two P-channel transistors and whose gate electrode receives the inverted AND-signal a_(i) ·b_(i), a parallel connection of two N-channel transistors which is connected in series with the parallel connection of the P-channel transistors forming said first output, the gate electrodes of said N-channel transistors receiving the bit signals a_(i) and b_(i), respectively, and a further N-channel transistor which is connected in series with the two parallel-connected N-channel transistors and whose gate electrode receives the inverted AND-signal a_(i) ·b_(i), the logic gate also comprising an inverter which is composed of a P- and an N-channel transistor and whose gate electrode is connected to the junction of said P- and N-channel transistors which forms the first output of the logic gate, the output of the inverter forming the second output of the logic gate.
 7. A logic full-adder circuit as claimed in claim 1, wherein the carry look-ahead signal circuit comprises a first series connection of transistors, gate electrodes of which receive the AND-signals a_(i) ·b_(i) for each of the pairs of like bit numbers with an ascending order, the transistor whose gate electrode receives the AND-signal a₀ ·b₀ of lowest order 0 being connected in series with a carry transistor whose gate electrode receives the carry signal c₀ having the order 0, one transistor of a plurality of transistors being connected in parallel with each section of the series connection of the carry transistor and m further transistors from said first series connection, m assuming any value from 1 to n, the gate electrode of said one transistor receiving the OR-signal a_(m-1) +_(m31)
 1. 8. A logic full-adder circuit as claimed in claim 7, wherein the transistors which are connected in series and in parallel in the carry look-ahead signal circuit are N-channel field-effect transistors which are connected in series with a single P-channel field-effect transistor between two power supply terminals. 